Computing View Graphs of Algebraic Surfaces

The "bad" directions or centres of projection, which yield degenerate projections of a smooth surface S embedded in 3-space, lie on a bifurcation set B of positive codimension in view space V (where V = 2 or 3 \ S). The connected components of V \ B are the nodes in the view graph of S, and two nodes are connected by an edge if the corresponding components are separated by a branch of B of dimension dim V - 1. The view graph of an algebraic surface of degree d has at most O(d10dim V) nodes. We describe an algorithm for computing the view graphs of surfaces defined as zero sets of polynomials with rational coefficients and present some examples